A263228 a(n) = 2*n*(16*n - 13).

0, 6, 76, 210, 408, 670, 996, 1386, 1840, 2358, 2940, 3586, 4296, 5070, 5908, 6810, 7776, 8806, 9900, 11058, 12280, 13566, 14916, 16330, 17808, 19350, 20956, 22626, 24360, 26158, 28020, 29946, 31936, 33990, 36108, 38290, 40536, 42846, 45220, 47658, 50160

Offset: 0

Author

Emeric Deutsch, Oct 13 2015

Keywords

• nonn
• easy

Comments

For n>=3, a(n) = the Wiener index of the Jahangir graph J_{4,n}. The Jahangir graph J_{4,n} is a connected graph consisting of a cycle graph C(4*n) and one additional center vertex that is adjacent to n vertices of C(4*n) at distances 4 to each other on C(4*n). In the Farahani reference the expression in Theorem 2 is accidentally incorrect; it should be 2*m*(16*m - 13).

The Hosoya polynomial of J_{4,n} is 5*n*x + n*(n+11)*x^2/2 + n*(2*n+1)*x^3 + n*(3*n-4)*x^4 + 2*n*(n-2)*x^5 + n*(n-3)*x^6/2 (see the Farahani reference, p. 234, last line; however, the expression in Theorem 1, p. 233, is accidentally incorrect).

Links

• M. R. Farahani, Hosoya polynomial and of Jahangir graphs J_{4,m}, Global J. Math, 3 (1), 232-236, 2015.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A049598, A263226, A263227, A263229, A263231.

Programs

Magma

[2*n*(16*n-13): n in [0..60]]; // Vincenzo Librandi, Oct 15 2015

Maple

seq(32*n^2 - 26*n, n=0..40);

Mathematica

Table[2 n (16 n - 13), {n, 0, 40}] (* Bruno Berselli, Oct 15 2015 *)

PARI

vector(50, n, n--; 2*n*(16*n-13)) \\ Altug Alkan, Oct 15 2015

Formula

G.f.: 2*x*(3+29*x)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).